2.随机梯度下降.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4fcd93aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1503, 5), (1503,))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "#加载数据\n",
    "data = np.loadtxt(fname='./线性数据.csv', delimiter='\\t')\n",
    "\n",
    "#标准化\n",
    "data -= data.mean(axis=0)\n",
    "data /= data.std(axis=0)\n",
    "\n",
    "x = data[:, :-1]\n",
    "y = data[:, -1]\n",
    "\n",
    "x.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cc6c8e3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#常量\n",
    "N, M = x.shape\n",
    "\n",
    "#变量\n",
    "w = np.ones(M)\n",
    "b = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "92163201",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6590042695516539"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#预测函数\n",
    "def predict(x):\n",
    "    return w.dot(x) + b\n",
    "\n",
    "\n",
    "predict(x[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7bb7a80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21258140154187247"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#求loss,MSELoss\n",
    "def get_loss(x, y):\n",
    "    pred = predict(x)\n",
    "    loss = (pred - y)**2\n",
    "    return loss\n",
    "\n",
    "\n",
    "get_loss(x[0], y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8027d213",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.61003339, -1.05581946,  1.66242713,  1.21242212, -0.59417855]),\n",
       " 0.923131013558981)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_gradient(x, y):\n",
    "    global w\n",
    "    global b\n",
    "\n",
    "    eps = 1e-3\n",
    "\n",
    "    loss_before = get_loss(x, y)\n",
    "\n",
    "    gradient_w = np.empty(M)\n",
    "    for i in range(M):\n",
    "        w[i] += eps\n",
    "        loss_after = get_loss(x, y)\n",
    "        w[i] -= eps\n",
    "        gradient_w[i] = (loss_after - loss_before) / eps\n",
    "\n",
    "    b += eps\n",
    "    loss_after = get_loss(x, y)\n",
    "    b -= eps\n",
    "    gradient_b = (loss_after - loss_before) / eps\n",
    "\n",
    "    return gradient_w, gradient_b\n",
    "\n",
    "\n",
    "get_gradient(x[0], y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f39e0125",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11073.905141728206"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def total_loss():\n",
    "    loss = 0\n",
    "    for i in range(N):\n",
    "        loss += get_loss(x[i], y[i])\n",
    "    return loss\n",
    "\n",
    "\n",
    "total_loss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c371c6a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 11038.895201527894\n",
      "150 6696.3736283721655\n",
      "300 4354.119709336485\n",
      "450 3004.4953025777063\n",
      "600 2310.68634531403\n",
      "750 1839.580107951638\n",
      "900 1549.8047186884628\n",
      "1050 1278.2079624059054\n",
      "1200 1099.1810250366634\n",
      "1350 986.6025037947752\n",
      "1500 921.4757031198328\n",
      "1650 879.159069825457\n",
      "1800 853.2767252227716\n",
      "1950 835.2496534941863\n",
      "2100 812.3758750332744\n",
      "2250 794.1165878394305\n",
      "2400 786.9647280480957\n"
     ]
    }
   ],
   "source": [
    "plt_x = []\n",
    "plt_y = []\n",
    "for epoch in range(2500):\n",
    "    i = np.random.randint(N)\n",
    "    gradient_w, gradient_b = get_gradient(x[i], y[i])\n",
    "    w -= gradient_w * 1e-3\n",
    "    b -= gradient_b * 1e-3\n",
    "\n",
    "    plt_x.append(epoch)\n",
    "    plt_y.append(total_loss())\n",
    "\n",
    "    if epoch % 150 == 0:\n",
    "        print(epoch, total_loss())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0471a70d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.plot(plt_x, plt_y)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}